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I am stuck in trying to inverse this function:

$f(x) = x-(x-0.75)^2+a\ln((x-0.75)^2+1)$

Where $x\in(0.75;1.25)$.

Does anybody has an idea of the solution? Is there a method you advice? I tried on wolfram alpha, but it is not finding any solution.

Many thanks!

Erik M
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Du Bois Eloi
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  • First of all have you checked that the function is bijective on the given interval whatever the value of $a$ ? Then, it is almost sure that there is no explicit expression for the inverse function. – Jean Marie Dec 15 '16 at 21:59
  • Thank you for your answer, I need to work a bit more on this. Many thanks. – Du Bois Eloi Dec 15 '16 at 22:08

1 Answers1

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Most likely, the inverse function (if it exists, I didn't check this) cannot be written using elementary functions, as you would need to solve the equation for x.